I drew some lines in a GIS application in this projection:
+proj=longlat+ellps=WGS84 +datum=WGS84 - is there a name for this projection?

I imported my lines into R and to prepare for calculating distance between points on my lines, I projected my lines using:
+proj=laea +lat_0=52 +lon_0=10 +x_0=4321000 +y_0=3210000 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs - again, is there a name for this projection?

To actually calculate distances between points on my lines, I used the gLength function in the R package rgeos. What sort of distance calculation does gLength use?

1 Answer
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+proj=longlat +datum=WGS84 is a coordinate reference system (crs). If you would create a map with that, by treating longitude as 'x' and latitude as 'y', you could call it the equirectangular projection.

+proj=laea stand for "Lambert Equal Area". This is planar (Cartesian) crs (unlike angular longlat), and can be used with rgeos::gLenght. gLength computes the shortest distance, between points along the line.